Selection bias occurs when your sample is truncated and the cause of that truncation is correlated with your dependent variable. Ignoring the correlation, the model could be estimated using least squares or truncated least squares. In either case, obtaining consistent estimates of the regression parameters is not possible. In this section the basic features of the this model will be presented.

Consider a model consisting of two equations. The first is the selection equation, defined

z* = Yi + Y2Wi + Ui, i = 1,… ,N

where z* is a latent variable, Yi and y2 are parameters, wi is an explanatory variable, and ui is a random disturbance. A latent variable is unobservable, but we do observe the dichotomous variable

The second equation, called the regression equation, is the linear model of in...

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